Researchers apply high-order structure to link prediction to capture the topology information around the target link. For example, similarity metrics CAR[1]} and CCLP[2]} use the triangle structure, which gave some insights into the mechanism of high-order interaction. But such methods mainly focus on the quantity information of triangles, while ignoring the interaction information between different structures. Simplex has been used in the study of complex dynamical systems due to its powerful mathematical representation[3]}.
